A384997 - OEIS

A384997

Numbers m such that phi(m) is a heptagonal number.

1, 2, 19, 27, 38, 54, 113, 145, 149, 226, 232, 290, 298, 348, 361, 541, 589, 617, 667, 722, 813, 837, 891, 971, 1082, 1084, 1178, 1234, 1289, 1334, 1363, 1501, 1626, 1674, 1782, 1783, 1942, 2133, 2357, 2578, 2726, 3002, 3011, 3187, 3566, 3869, 4069, 4266, 4685, 4714, 4823

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Table of n, a(n) for n=1..51.

EXAMPLE

Since phi(54) = 18 = (5 * 3^2 - 3 * 3) / 2, a heptagonal number, 54 is a term of this sequence.

MATHEMATICA

Select[Range[5000], IntegerQ[(3 + Sqrt[9 + 40 EulerPhi[#]])/10] &]

PROG

(PARI) isok(m) = ispolygonal(eulerphi(m), 7); \\ Michel Marcus, Sep 09 2025

(Python)

from math import isqrt

from sympy import totient as phi

ok = lambda n: (d:=9+40*phi(n)) == (s:=isqrt(d))**2 and (3+s)%10==0

print([m for m in range(1, 5000) if ok(m)]) # Aidan Chen, Sep 19 2025

CROSSREFS

Cf. A000010, A000566, A384996.

Sequence in context: A031030 A083689 A390136 * A102617 A365235 A290163

Adjacent sequences: A384994 A384995 A384996 * A384998 A384999 A385000

KEYWORD

nonn,easy

AUTHOR

Aidan Chen, Sep 07 2025

STATUS

approved